0% integrity is actually hull at 70% strength I believe...
Regarding danger, I prefer the term challenge. There can be no actual danger in the game, destruction isn't dangerous, just a time sink so frustrating, and as you absolutely correctly (IMO) point out, random destruction would be the worst thing FD could put into the game. I mean, none of us really enjoy the RNG in the game do we?
However, challenge in the game, challenge that can be recognized and can be mitigated by a players actions would be great. Common exploration questions are "should I take heat sinks or an AFMU?", and many explorers just go "meh, I never do, you never need 'em". But we should! And their use should enable explorers to potentially stay out longer, take challenging risks and overcome unexpected challenging events.
Regarding integrity, since it can only be repaired at a station, while it absolutely should make a difference, really all that would do is mean explorers would have to return to civilization more often and I'm not sure I see the added game-play there. IMHO, risks and challenge need to have an active counter to them, not simply a passive one, so there would need to be a way of shoring up your ship's integrity if it's allowed to cause catastrophic consequences, at least somewhat while out in the black.
TL : DR - Challenge in exploration (everywhere in the game) should have an active counter to it. A player should be able to mitigate and overcome the challenge by active game-play. Having random challenge that simply swipes players for no reason and gives them no recourse to be able to overcome it, while that might be something we have to accept in real life, would be tedious in a game.